We propose a quantum version of the well known minimum distance classification model called Nearest Mean Classifier (NMC). In this regard, we presented our first results in two previous works. First, a quantum counterpart of the NMC for two-dimensional problems was introduced, named Quantum Nearest Mean Classifier (QNMC), together with a possible generalization to any number of dimensions. Seco...

In this paper we introduce a minimum barrier distance, MBD, defined for the (graphs of) real-valued bounded functions fA, whose domain D is a compact subsets of the Euclidean space R. The formulation of MBD is presented in the continuous setting, where D is a simply connected region in R, as well as in the case where D is a digital scene. The MBD is defined as the minimal value of the barrier s...

A method is presented for incorporating error correction using a minimum distance measure into LR parsers. The method is suitable for use by an automatic parser-generator. State information in the LR parser stack at the point of detection of error is used to generate a set of strings which are potential repairs to the input. A string with least minimum distance from the actual input is chosen a...

Some of the following problems look similar to the MAD Triangulation problem, but we have not found any deep connections: •Minimum Average Distance Spanning Subgraph in a budgeted version [2] was studied in the context of network design (minimizing average routing time). The problem is NP-complete even with unit weights. •Minimum Average Distance Spanning Tree [1]. NP-completeness is implied by...

We study the r-th generalized minimum distance function (gmd function for short) and the corresponding generalized footprint function of a graded ideal in a polynomial ring over a field. If X is a set of projective points over a finite field and I(X) is its vanishing ideal, we show that the gmd function and the Vasconcelos function of I(X) are equal to the r-th generalized Hamming weight of the...

Suppose we have a concatenated code where the outer code is an [N,K,D]Q code, and the inner code is an [n, k, d]q code, with Q = q. In section 4 we will see that the concatenated code is actually an [Nn,Kk, Dd]q code, but for now we will show the weaker property that it is an [Nn,Kk, Dd/2]q. Consider the näıve decoding procedure which uses the inner decoding scheme on each received symbol, then...